Question

1. Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled.

The sum is 4, given that the green one is either 2 or 3.

Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled.

The sum is 10, given that the dice have opposite parity.

Answer 1

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Sol:- thet event that the green dice is eilter 2 0r3 = x sample space of x= 5 ) 2,2)(2,3)(274)(2,5) (2,6)(3,1)? f3/2) (3,3)(3,4)(3,5)(3,6) → No.of element = 12. event that sum is 4 =Y Sample space of y = $(212),(310) (1,3)} Sample space of (yox) = $12/27 (310) } No.of elements = 2 conditional probability that the sum is 4 given that the green one is either 2003 = P(1/2) = ? 1 PX = 1 =10.167] opposite parity (one die showing even, another odd) choices - Red - 13,5 green - 2,4,6 possible out comes $(1,2)(6,4) (6) (3,2) (3,4)(3;6)6,215,4) Plynx) - PY/2) - 2) (516) S . No. of elements = 9 Out of 9 outcomes, how many have sum 10 is = Zero probability of the sum being 10 is = o to