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probability:02_multiple_event_probability [2014/01/20 13:48] marje [2.2. Mutually non exclusive events] |
probability:02_multiple_event_probability [2014/01/20 15:44] marje [2.3. Independent events] |
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| $\text{Pr}[\text{"we obtain two tails in a row"}]=$ | $\text{Pr}[\text{"we obtain two tails in a row"}]=$ | ||
| - | $\text{Pr}[\text{"1st throw gives tails"}\cap\text{"2nd throw gives tails"}]= | + | $\text{Pr}[\text{"1st throw gives tails"}\cap\text{"2nd throw gives tails"}]=$ |
| - | \text{Pr}[\text{"1st throw gives tails"}]\cdot\text{Pr}[\text{"2nd throw gives tails"}]= | + | |
| + | $\text{Pr}[\text{"1st throw gives tails"}]\cdot\text{Pr}[\text{"2nd throw gives tails"}]= | ||
| \frac{1}{2}\cdot\frac{1}{2}= | \frac{1}{2}\cdot\frac{1}{2}= | ||
| \frac{1}{4}.$ | \frac{1}{4}.$ | ||
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| Or, by tossing a coin and rolling a six-faced normal dice, the probability | Or, by tossing a coin and rolling a six-faced normal dice, the probability | ||
| - | $\text{Pr}[\text{"we land on heads"}\cap\text{"we roll a six"}]= | + | $\text{Pr}[\text{"we land on heads"}\cap\text{"we roll a six"}]=$ |
| - | \text{Pr}[\text{"we land on heads"}]\cdot\text{Pr}[\text{"we roll a six"}]=\frac{1}{2}\cdot\frac{1}{6}= | + | $\text{Pr}[\text{"we land on heads"}]\cdot\text{Pr}[\text{"we roll a six"}]=\frac{1}{2}\cdot\frac{1}{6}= |
| \frac{1}{12}.$ | \frac{1}{12}.$ | ||