A random variable X has the following probability distribution
X= x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
P(X = x) | 0.15 | 0.23 | k | 0.10 | 0.20 | 0.08 | 0.07 | 0.05 |
For the events E = {x/x is a prime number} and F = {x/x <4} then P(E ∪ F)
0.57
0.87
0.77
0.35
The correct option is: (C) 0.77
Let \( F \) and \( F' \) be the foci of the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) (where \( b<2 \)), and let \( B \) be one end of the minor axis. If the area of the triangle \( FBF' \) is \( \sqrt{3} \) sq. units, then the eccentricity of the ellipse is:
A common tangent to the circle \( x^2 + y^2 = 9 \) and the parabola \( y^2 = 8x \) is
If the equation of the circle passing through the points of intersection of the circles \[ x^2 - 2x + y^2 - 4y - 4 = 0, \quad x^2 + y^2 + 4y - 4 = 0 \] and the point \( (3,3) \) is given by \[ x^2 + y^2 + \alpha x + \beta y + \gamma = 0, \] then \( 3(\alpha + \beta + \gamma) \) is: