From a school team of 100 students, the number of right-handed batsmen and left- handed batsmen are 35 and 65 respectively. What would be the probability of getting a right-handed and left-handed batsman as openers if the batsman is selected at
random.
Answers
Given : a school team of 100 students, the number of right-handed batsmen and left-handed batsmen are 35 and 65 respectively.
To Find : What would be the probability of getting a right-handed and left-handed batsman as openers
Solution:
Total = 100
Right Hand (RH) = 35
Left Hand ( LH) = 65
2 Openers out of 100 can be selected in ¹⁰⁰C₂ ways
= 4950
1 Openers out of 35 RH can be selected in ³⁵C₁ ways
1 Openers out of 65 LH can be selected in ⁶⁵C₁ ways
Total Ways of Selecting 1 RH & 1 LH = ³⁵C₁ x ⁶⁵C₁
= 35 x 65
Probability = 35 x 65 / 4950
= 7 x 65 / 990
= 7 x 13 / 198
= 91/198
probability of getting a right-handed and left-handed batsman as openers = 91/198
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