Question

The table shows the results of a survey that asked the members of a swim team what stroke they like:

Female

Butterfly 321

Backstroke 125

Breast Strokes 456

Free Style 684

Male

Buttlerfly 503

Backstorke 211

Breaststroke 367

Freestyle 724

a. likes breastroke or is female

b. likes backstorke and is male

c. likes butterfly, given that the person is a male

Answer 1

NOTE: If all the events happen (an "and question") Multiply the probabilities together. If only one of the events happens (an "or question") Add the probabilities together

	Female	Male	TOTALS	Prob(F)	Prob(M)
Butterfly	321	503	824	0.20	0.28
Backstroke	125	211	336	0.08	0.12
Breaststroke	456	367	823	0.29	0.20
Free Style	684	724	1408	0.43	0.40
TOTAL	1586	1805	3391	1	1

P(butterfly)=	0.24
P(backstroke)=	0.10
P(breaststroke)=	0.24
P(free Style)=	0.42

A) Or means that the outcome has to satisfy one condition, or the other condition, or both at the same time.

= P(likes beaststroke) + P(is a female) + P(likes beastroke and is a female)

= 0.24 + 0.5 + 0.29

=1.03

B) And means that the outcome has to satisfy both conditions at the same time.

= P(likes BackStroke and is Male)

= 0.12

C) = P(Butterfly | Male) = 0.28