Question #4133
Three groups if children contains respectively 3 girls and 1 boy, 2 girls and 2 boys, and 1 girl and 3 boys. One child is selected at random from each group. Show that the chance that 3 selected consists of 1 girl and 2 boys is 13/32.
Expert's answer
The probability of selecting of 1 boy from the first group is 1/4, 1 girl 3/4
The probability of selecting of 1 boy from the second group is 1/2, 1 girl 1/2
The probability of selecting of 1 boy from the third group is 3/4, 1 girl 1/4.
The probability of selecting of 1 girl and 2 boys is
P(girl from I group) AND P(boy from II group) AND P(boy from III group) OR
P(boy from I group) AND P(girl from II group) AND P(boy from III group) OR
P(boy from I group) AND P(boy from II group) AND P(girl from III group)
In Math it equals to (AND = "*", OR = "+"):
3/4*1/2*3/4 + 1/4*1/2*3/4 + 1/4*1/2*1/4 = 9/32 + 3/32 + 1/32 = 13/32
The probability of selecting of 1 boy from the second group is 1/2, 1 girl 1/2
The probability of selecting of 1 boy from the third group is 3/4, 1 girl 1/4.
The probability of selecting of 1 girl and 2 boys is
P(girl from I group) AND P(boy from II group) AND P(boy from III group) OR
P(boy from I group) AND P(girl from II group) AND P(boy from III group) OR
P(boy from I group) AND P(boy from II group) AND P(girl from III group)
In Math it equals to (AND = "*", OR = "+"):
3/4*1/2*3/4 + 1/4*1/2*3/4 + 1/4*1/2*1/4 = 9/32 + 3/32 + 1/32 = 13/32
Learn more about our help with Assignments: Statistics and Probability
