Question # 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

Normal distributions
ANSWERED 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 $$P(E_1)=0.2,P(E_2)=0.3,$$ and $$P(E_3)=0.4$$. The probability of outcome $$E_4$$ is ?
3) If A and B are mutually exclusive events with $$P(A) = 0.3$$ and $$P(B) = 0.5$$, then $$P(A\cap B) =?$$
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 ? 2021-06-08

1) Since events are mutually exclusive : $$P(A \cap B) =0$$
and $$P(A \cup B) =P(A)+P(B)-P(A \cap B) =0.3+0.5-0 =0.8$$
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 $$P(A \cap B)$$ ; 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