250 people on a plane; 120 speak english;150 speak spanish; 30 speak neither. what probability speak English and Spanish ?
To find the probability of someone on the plane speaking both English and Spanish, we need to know the number of people who speak both languages. However, the given information only tells us the total number of people who speak each language separately.
To solve this problem, we can use the principle of inclusion-exclusion. We start by adding the number of people who speak English (120) and the number of people who speak Spanish (150):
120 + 150 = 270
However, this counts the individuals who speak both English and Spanish twice. To correct this, we need to subtract the number of people who speak both languages:
270 - 250 = 20
Now we have the number of individuals who speak both English and Spanish, which is 20. To find the probability, we divide this number by the total number of people on the plane (250):
P(Speaking English and Spanish) = 20/250 = 0.08 or 8%
Therefore, the probability of a person on the plane speaking both English and Spanish is 8%.