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P(A and B) expressed in the simplest form is (B) 2/21.
What is probability?
- Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true.
- The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
To express P(A and B) in the simplest form:
- P(A and B) means that you need to multiply the two probabilities together since both A and B need to happen.
- The probability of drawing a black tile on the first draw is 4/15 since there are 15 total tiles and 4 of those are black.
- On the second draw, the bag is already missing a tile, and there are therefore 14 tiles remaining.
- For the second one, the probability is 5/14, since there are 14 total tiles and 5 of them are white.
- Multiplying these two together, we get 4/15 × 5/14 = 20 / 210 = 2/21.
Therefore, P(A and B) expressed in the simplest form is (B) 2/21.
Know more about probability here:
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The complete question is given below:
A bag contains 4 black tiles, 5 white tiles, and 6 blue tiles. Event A is defined as drawing a black tile from the bag on the first draw, and event B is defined as drawing a white tile on the second draw.
If two tiles are drawn from the bag, one after the other without replacement, what is P(A and B) expressed in the simplest form?
A. 4/45
B. 2/21
C. 4/15
D. 5/14
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