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A picnic was arranged for the members of a club. The organizer started calling all the members to find how many members would be taking part in the picnic. She could not contact 20% of them. Of the remaining members, 15% did not wish to take part and the rest wanted more time to decide. Finally, 80% of those who wanted more time to decide ended up going to the picnic.

If a member is picked up at random, the probability that he or she needed more time to decide and finally did not attend the picnic is ?%, and the probability that he or she was contacted but did not attend the picnic is ?%

Respuesta :

MrEquation
Answer: 13.6% needed more time but then said no. 25.6% were contacted but said no.

To do this problem, you have to create a tree diagram with all of the possibilities.

The first branch separates with 20% not being contacted and 80% being contacted.

Then, the 80% branch can be broken into 12% saying no and 68% needing more time (multiply by 15% and 85%).

Then, the 68% branch can be broken into 54.4% going and 13.6 not going (multiply by 80% and 20%).

With the tree diagram, just pick the percents that you need.

Answer:

The probability that he or she needed more time to decide and finally did not attend the picnic is :  13.6%

The probability that he or she was contacted but did not attend the picnic is : 25.6%

Step-by-step explanation:

Let P denote the probability of an event.

Now, it is given that:

  • 20% were not contacted.
  • This means that 80% were contacted.
  1. Out of these 80% ; 15% did not want to take part.
  2. While out of remaining 85% of 80%  wanted to decide

→ At last 80% of 85% of 80% decided to go for picnic.

→ while 20% of 85% of 80% decided not to go to the picnic.

This means that:

The probability that he or she needed more time to decide and finally did not attend the picnic is :  (0.20×0.85×0.80)×100=13.6%

The probability that he or she was contacted but did not attend the picnic is :  [(0.80×0.85×0.20)+(0.80×0.15)]×100=25.6%