See below for the values of the probabilities
<h3>How to determine the probabilities?</h3>
<u>The probabilities of the whole events</u>
For event A, the probability of the whole event is calculated using
P(A) = n(A)/Total
Using the table of values, we have:
P(F) = 130/200 = 0.65
P(M) = 70/200 = 0.35
P(L) = 60/200 = 0.30
P(S) = 40/200 = 0.20
<u>The probabilities of the intersection events</u>
For events A and B, the probability of the intersection events is calculated using
P(A n B) = n(A n B)/Total
Using the table of values, we have:
P(F n E) = P(E n F) = 60/200 = 0.30
P(F n L) = P(L n F) = 40/200 = 0.20
P(F n S) = P(S n F) = 30/200 = 0.15
P(M n E) = P(E n M) = 40/200 = 0.20
P(M n L) = P(L n M) = 20/200 = 0.10
P(M n S) = P(S n M) = 10/200 = 0.05
<u>The probabilities of the Union (OR) disjoint events</u>
For events A and B, the probability of the union (OR) disjoint events is calculated using
P(A u B) = P(A) + P(B)
Using the table of values, we have:
P(E u S) = P(E) + P(S) = 100/200 + 40/200 = 0.70
P(E u L) = P(E) + P(L) = 100/200 + 60/200 = 0.80
P(E u L u S) = P(E) + P(L) + P(S) = 100/200 + 60/200 + 40/100 = 1
P(F u M) = P(F) + P(M) = 130/200 + 70/200 = 1
<u>The probabilities of the Union (OR) joint events</u>
For events A and B, the probability of the union (OR) joint events is calculated using
P(A u B) = P(A) + P(B) - P(A n B)
Using the table of values, we have:
P(E u F) = P(E) + P(F) - P(E n F) = 100/200 + 130/200 - 60/100 = 0.85
P(L u M) = P(L) + P(M) - P(L n M) = 60/200 + 70/200 - 20/100 = 0.55
<u>The probabilities of the conditional probabilities</u>
For events A and B, the conditional probability is calculated using
P(A/B) = P(A n B)/P(B)
Using the table of values, we have:
P(F/S) = P(F n S)/P(S) = 0.15/0.20 = 0.75
P(F/E) = P(F n E)/P(E) = 0.30/0.50 = 0.60
P(M/S) = P(M n S)/P(S) = 0.05/0.20 = 0.25
P(M/L) = P(M n L)/P(L) = 0.10/0.30 = 0.33
P(S/F) = P(F n S)/P(F) = 0.15/0.65 = 0.23
P(E/F) = P(F n E)/P(F) = 0.30/0.65 = 0.46
P(S/M) = P(M n S)/P(M) = 0.05/0.35 = 0.14
P(L/M) = P(M n L)/P(M) = 0.10/0.35 = 0.29
<u>The multiplication of dependent events</u>
For events A and B, the conditional probability is calculated using
P(A n B) = P(A) * P(B/A)
Using the table of values, we have:
P(F n L) = P(F) * P(L/F)
This gives
P(F n L) = 0.65 * (0.20/0.30)
Evaluate
P(F n L) = 0.43
Read more about probabilities at:
brainly.com/question/25870256
#SPJ1