The probability that the spinner lands on an odd space given that it lands on the white space is 3/8.
The question is incomplete and the possible question is
The spinner given in the below image is spun. Find the probability that it lands on an odd number, given that it lands on white space.
The conditional probability of an event B on the hypothesis that another event A has occurred will be denoted by P(B|A) and defined by
P(B|A)=P(AB)/P(A)
provided P(A)≠0.
In case P(A)=0, the conditional probability remains undefined.
The sample space has 16 events, out of which 8 events have white space.
And out of those 8 white spaces, 3 have odd numbers.
White events are 12,14,6,2,10,15,3,9.
White odd events are 3,9,15.
Hence, P(White odd)=3/16
P(White)=8/16=1/2
Thus, the probability that the spinner lands on an odd space given that it lands on the white space
=P(odd | White)
=P(White odd) / P(White)
=(3/16)/(1/2)
=3/8
Hence, the probability that the spinner lands on an odd space given that it lands on the white space is 3/8.
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