# 1) If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A\cap B)=? 2) An experiment consists of four outcomes with P(E_1)=0

Daniaal Sanchez 2021-06-07 Answered

1) If A and B are mutually exclusive events with $P\left(A\right)=0.3$ and $P\left(B\right)=0.5$, then $P\left(A\cap B\right)=?$
2) An experiment consists of four outcomes with $P\left({E}_{1}\right)=0.2,P\left({E}_{2}\right)=0.3,$ and $P\left({E}_{3}\right)=0.4$. The probability of outcome ${E}_{4}$ is ?
3) If A and B are mutually exclusive events with $P\left(A\right)=0.3$ and $P\left(B\right)=0.5$, then $P\left(A\cap B\right)=?$
4) The empirical rule states that, for data having a bell-shaped distribution, the percentage of data values being within one standard deviation of the mean is approximately
5) If a penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is ?

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lamusesamuset

1) Since events are mutually exclusive : $P\left(A\cap B\right)=0$
and $P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)=0.3+0.5-0=0.8$
2) since sum of all events is 1
$P\left(E4\right)=1-0.2-0.3-0.4=0.1$
3) here sign is missing , instead ? is given in question: if it is $P\left(A\cap B\right)$ ; then it is 0
4) percentage of data values being within one standard deviation of the mean is approximately =68
5) probability of heads on the fifth trial is =0.5