Question

in Pennsylvania Cash 5 lottery balls are numbered 1 to 43 right balls are selected does not replacement the order in which the balls are selected does not matter the term your probability of winning Pennsylvania Cash 5 with one ticket write your answers in fractions

Answer 1

Probability = Favourable outcomes / Total outcomes.

When picking without replacement, each time the favourable outcome and the total outcomes reduces by 1.

There are 5 winning numbers which needs to be picked out from 43 balls)

P(Picking the 1st winning number) = 5/43

P(Picking the 2nd winning number) = 4/42

P(Picking the 3rd winning number) = 3/41

P(Picking the 4th winning number) = 2/40

P(Picking the 5th winning number) = 1/39

Therefore the required probability = (5/43) * (4/42) * (3/41) * (2/40) * (1/39) = 1/962598

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Another method is using combinations. Since order is not important, there is only one favourable outcome, which is getting these 5 numbers. the total outcomes is getting any 5 out of the 43 numbers in ⁴³C₅ = 962958 ways.

Therefore the required probability = 1/962598

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