Three unbiased coins are tossed.What is the probability of getting at least 2 he

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Question
Three unbiased coins are tossed.What is the probability of getting at least 2 heads?
Options
A. 1/4
B. 1/2
C. 3/4
D. 1/3

Correct Answer

1/2

Explanation

Here S= {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}.

Let E = event of getting at least two heads = {THH, HTH, HHT, HHH}.

P(E) = n(E) / n(S)

= 4/8= 1/2

Probability problems

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1. A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Options
A. 3/7
B. 4/7
C. 1/8
D. 3/4

Discuss

2. Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:
Options
A. 3/20
B. 29/34
C. 47/100
D. 13/102

Discuss

3. A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what is the probability that either both are oranges or both are non defective?
Options
A. 136/345
B. 17/87
C. 316/435
D. 158/435

Discuss

Correct Answer: 316/435

Explanation:

$n (s) = {}^{30}C_{2}$

Let A be the event of getting two oranges and

B be the event of getting two non-defective fruits.

and $(A ? B)$ be the event of getting two non-defective oranges

$? P (A) = \frac{{}^{20}C_{2}}{{}^{30}C_{2}}, P (B) = \frac{{}^{22}C_{2}}{{}^{30}C_{2}} a n d P (A ? B) = \frac{{}^{15}C_{2}}{{}^{30}C_{2}}$

$? P (A ? B) = P (A) + P (B) - P (A ? B)$

= $\frac{{}^{20}C_{2}}{{}^{30}C_{2}} + \frac{{}^{22}C_{2}}{{}^{30}C_{2}} - \frac{{}^{15}C_{2}}{{}^{30}C_{2}} = \frac{316}{435}$

5. A letter is takenout at random from 'ASSISTANT' and another is taken out from 'STATISTICS'. The probability that they are the same letter is :
Options
A. 35/96
B. 19/90
C. 19/96
D. None of these

Discuss

Correct Answer: 19/90

Explanation:

$A S S I S T A N T ? A A I N S S S T T$

$S T A T I S T I C S ? A C I I S S S T T T$

Here N and C are not common and same letters can be A, I, S, T. Therefore

Probability of choosing A = $\frac{2_{C_{1}}}{9_{C_{1}}} � \frac{1_{C_{1}}}{10_{C_{1}}}$ = 1/45

Probability of choosing I = $\frac{1}{9_{C_{1}}} � \frac{2_{C_{1}}}{10_{C_{1}}}$ = 1/45

Probability of choosing S = $\frac{3_{C_{1}}}{9_{C_{1}}} � \frac{3_{C_{1}}}{10_{C_{1}}}$ = 1/10

Probability of choosing T = $\frac{2_{C_{1}}}{9_{C_{1}}} � \frac{3_{C_{1}}}{10_{C_{1}}}$ = 1/15

Hence, Required probability = $\frac{1}{45} + \frac{1}{45} + \frac{1}{10} + \frac{1}{15} = \frac{19}{90}$

6. One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
Options
A. 3/13
B. 1/13
C. 3/52
D. 9/52

Discuss

7. 8 couples (husband and wife) attend a dance show "Nach Baliye' in a popular TV channel ; A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is atleast one couple will be selected is :
Options
A. 8/39
B. 15/39
C. 12/13
D. None of these

Discuss

8. If two letters are taken at random from the word HOME, what is the probability that none of the letters would be vowels?
Options
A. 1/6
B. 1/2
C. 1/3
D. 1/4

Discuss

9. In a class, 30% of the students offered English, 20% offered Hindi and 10% offered both. If a student is selected at random, what is the probability that he. has offered English or Hindi ?
Options
A. 1/2
B. 3/4
C. 4/5
D. 2/5

Discuss

10. A bag contains 2 red Roses, 4 yellow Roses and 6 pink Roses. Two roses are drawn at random. What is the probability that they are not of same color?
Options
A. 1/6
B. 2/3
C. 14/33
D. 5/6

Discuss

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Three unbiased coins are tossed.What is the probability of getting at least 2 heads?

Probability problems

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Three unbiased coins are tossed.What is the probability of getting at least 2 heads?

Probability problems

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Programming

Reasoning

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