1) If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then

1) If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then $$\displaystyle{P}{\left({A}\cap{B}\right)}=?$$
2) An experiment consists of four outcomes with $$\displaystyle{P}{\left({E}_{{1}}\right)}={0.2},{P}{\left({E}_{{2}}\right)}={0.3},$$ and $$\displaystyle{P}{\left({E}_{{3}}\right)}={0.4}$$. The probability of outcome $$\displaystyle{E}_{{4}}$$ is ?
3) If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then $$\displaystyle{P}{\left({A}\cap{B}\right)}=?$$
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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crocolylec
1) Since events are mutually exclusive : P(A n B) =0
and P(A u B) =P(A)+P(B)-P(A n B) =0.3+0.5-0 =0.8
2) since sum of all events is 1
P(E4) =1-0.2-0.3-0.4 =0.1
3) here sign is missing , instead ? is given in question: if it is P(A n B) ; 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