just multiply the chance by each other
0.7 x 0.7 x 0.7 = 0.343
Answer: The required probability that all three friends will say they can go to the mall with us is 0.343.
Step-by-step explanation: Given that we are asking three friends to go to the mall. The probability of saying yes by each of the friends is 0.7.
We are to find the probability that all three friends will say they can go to the mall with us.
Let, E, E' an E'' represents the events that the first friend say yes, second friend say yes and third friend say yes for going to the mall.
Then,
[tex]P(E)=0.7,~~~P(E')=0.7,~~~P(E'')=0.7.[/tex]
Since the chance of saying yes by any of the friend does not depend on the decision of the other two friends. So, the three events E, E' and E'' are independent of each other.
Therefore, the probability that all three friends will say they can go to the mall with us is given by
[tex]P(E\cap E'\cap E'')=P(E)\times P(E')\times P(E'')=0.7\times 0.7\times 0.7=0.343.[/tex]
Thus, the required probability is 0.343.
