Will Santa Deliver?

Probability Level 2

The probability for Santa to successfully deliver the presents for a day is $0.6$ . If Santa is required to deliver the presents for 5 days, find the probability that Santa will at least successfully delivers the presents on one of the 5 days.

Round your answer to 2 decimal places.

The answer is 0.99.

1 solution

Geoff Pilling
Dec 6, 2016

There are two approaches to this problem:

Counting the number of ways he could get at least one successful deliveries, and turning this into a probability.
Counting the number of ways he doesn't get any successful deliveries, turning this into a probability that is subtracted from 1 to get the answer.

I chose to use the latter, since it is much easier to calculate, as there is only one way that he can get no successful deliveries, (vs. $31$ ways he can get at least one non successful delivery).

To get no successful deliveries, the probability is $(0.4)^5$ since he needs to fail to deliver on each of the five occasions and he has $0.4$ chance to fail on each one.

The probability that he gets at least one successful delivery is one minus the probability he gets no successful deliveries $(0.4)^5$ , so

$P = 1 - (0.4)^5 = \boxed{0.99}$

Would it be possible to add justification why you went with counting no successful deliveries? (That is, note that there are lots of ways a run with at least one success can happen like WLLWL or LWWLW but only one way LLLLL of failing all the times, so it's easier to count.)

Jason Dyer Staff - 4 years, 6 months ago

Done ...............

Geoff Pilling - 4 years, 6 months ago

Will Santa Deliver?

The answer is 0.99.

1 solution

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