Binoculars Express

Probability Word Problem Help please!?

Among 170 households surveyed, 43 have a video camera, 44 have a snapshot camera, 48 have binoculars, 7 have video cameera and a snapshot camera, 8 have a snapshot camera and binoculars, and 4 have all three products. What is the probability that a household will have a snapshot camera or binoculars? Express the answer as a fraction.

Assuming that the list of results does not count the same household twice (that is, that the 43 with video cameras don’t include, for example, the ones with all three products), then the households in the following categories all have a snapshot camera or binoculars:

those that have a snapshot camera (44),
those that have binoculars (48),
those that have both (8), and
those that have all three products (4).

That’s 104, or 52/85 of the total.

Well, that isn’t one of the listed choices, so let’s assume that the counts of those with one product DO include those combining that product and others. (This is not a well-written question!)

If that’s the case, then we just add up the ones with binoculars (48) and the ones with a snapshot camera (44) and subtract the ones that have both (8) so as not to count them twice. That gives us 84, so it’s
84/170 = 42/85
which is answer c.

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