Q47 / 108 · NTA Abhyas (JEE Main) 2020 · Mathematics · Probability

A man alternately tosses a coin and throw a dice, beginning with the coin. The probability that he gets a head in coin before he gets a $5$ or $6$ in dice, is

Correct answer
A
$\frac{3}{4}$
B
$\frac{1}{2}$
C
$\frac{1}{3}$
D
$\frac{2}{3}$

Solution

A =

coin show head

B =

dice show

5

or

6

P (A) = \frac{1}{2}, P (B) = \frac{2}{6} = \frac{1}{3}

Hence, the required Probability

= P (A) + P (A^{C}) P (B^{C}) P (A) + {(P (A^{C}) P (B^{C}))}^{2} P (A) + \dots

= \frac{1}{2} + \frac{1}{2} \times \frac{2}{3} \times \frac{1}{2} + {(\frac{1}{2} \times \frac{2}{3})}^{2} \times \frac{1}{2} + \dots

= \frac{\frac{1}{2}}{1 - \frac{1}{3}} = \frac{\frac{1}{2}}{\frac{2}{3}} = \frac{3}{4}

Hence, the correct answer is option: 'A'.

More Probability Questions

Probability that A will pass the exam is 1 4 , B will pass the exam is 2 5 and C will pass the exam is 2 3 . The probability that exactly on
2 dice are thrown. Suppose a random variable X is assigned a value 2 k , if the sum on the dice is equal to k , then the expected value of X
A multiple-choice question has 5 options of which only one is correct. If a student does home work, then he is sure to identify the correct
If two distinct numbers a and b are selected from the set 5 1 , 5 2 , 5 3 . . . . . . . 5 9 , then the probability that log a b is an intege
A bag contains a mixed lot of red and blue balls. If two balls are drawn at random, the probability of drawing two red balls is five times t
Two persons A and B have equal number of sons. There are three cinema tickets which are to be distributed among sons of A and B . The probab